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create a dot plot of a sample of the population whose
mean is the same as the population mean.
your sample should have more than six, but fewer than
20 data points.
count
number
2
10
12
8
hean
10
12
8
mean
934
Answers
The 2nd dot plot in the attachment represents the dot plot that has the same sample mean as the population mean
How to create the dot plot?The dot plot that completes the question is added as an attachment.
Start by calculating the mean of the data plot using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
Substitute the values on the dot plot
[tex]\bar x = \frac{2*1+3*3+4*2+5+6*3+7*5+8*2+9*4+11*2+12*2}{25}[/tex]
[tex]\bar x = 7[/tex]
This means that the population mean of the dot plot is 7
Next, we create another dot plot that has the same mean as 7.
There are no direct rules to this, so we make use of the trial by error method.
After several attempts, we have the following frequency table:
Data point Frequency
2 1
3 2
4 0
5 4
6 5
7 2
8 5
9 0
10 2
12 3
The mean of the frequency table is:
[tex]\bar x = \frac{2 * 1 + 3 * 2 + 4 * 0 + 5 * 4 + 6 * 5 + 7 * 2 + 8 * 5 + 9 * 0 + 10 * 2 + 12 * 3}{1+2+0+4+5+2+5+0+2+3}[/tex]
Evaluate
[tex]\bar x = \frac{168}{24}[/tex]
Evaluate the quotient
[tex]\bar x = 7[/tex]
This means that the sample mean is 7 (same as the population mean)
Lastly, we represent the frequency table using a dot plot (the 2nd dot plot in the attachment)
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Related Questions
Given that XW bisects AXZ, what theorem or theorems could be used to justify that W is equidistant from the two outside rays?
Answers
Answer:
HA congruence postulate
Step-by-step explanation:
In order to show W is equidistant from A and Z, we must demonstrate that WA ≅ WZ. The HA congruence postulate can be used for that purpose.
__
proofWX bisects AXZ, so ∠WXA≅∠WXZ by the definition of an angle bisector. By the reflexive property of congruence, WX≅WX. The angles at A and Z are given as right angles.
So, we have triangles WAX and WZX that are right triangles with congruent hypotenuse and corresponding angle. These are the preconditions for the application of the HA congruence postulate. That postulate says the triangles WAX and WZX are congruent, so ...
WA ≅ WZ by CPCTC. Hence W is equidistant from the outside rays.
__
Additional comment
The definition of distance from a point to a line is the perpendicular distance from the point to the line. In this geometry, the perpendicular distances from W to the outside rays are the lengths of segments WA and WZ. That is why we need to show those lengths are the same.
The weight, w, that a horizontal beam can support varies inversely as the
length, l, of the beam. a beam measuring 5 meters in length can support
430 kilograms. how much weight can a beam measuring 2 meters
support?
Answers
A beam measuring 2 meters can support 172 kilograms
How to determine the weight?The variation is a direct variation.
So, we have:
w = kl
Where k is the constant of variation.
When l = 5, w = 430.
This means that:
430 = 5k
Divide both sides by 5
k = 86
So, we have:
w = 86l
When l = 2, we have:
w = 86 * 2
Evaluate
w = 172
Hence, a beam measuring 2 meters can support 172 kilograms
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1. You need a parking for your food truck, so you purchased 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours cost $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
2.If the weekday hours tripled but your budget of $220 for 26 parking hours remain the same. How many weekend hours can you purchase now that the weekday hours have increased?
Answers
The weekday hours you purchased is 5 hours.
The number of weekend hours I can purchase if the weekday hours tripled is 11 hours.
What are the linear equations that represent the question?2a + 10b = 220 equation 1
a + b = 26 equation 2
Where:
a = number of hours for weekday parking b = number of hours for weekend parkingHow many weekday hours did you purchase?
Multiply equation 2 by 10
10a + 10b = 260 equation 3
Subtract equation 3 from equation 2
8a = 40
a = 5 hours
What is the weekend hours I can purchase?
(5 x 3) + b = 26
15 + b = 26
b = 26 - 15
b = 11 hours
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A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP
Answers
The probability that he would have done at least this well if he had no ESP is 0.99979
What is the probability of determining that he would have done well with no ESP?To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]
There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
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In a group of 32 musicians, all play piano, guitar, or both. Of those musicians, 12 only play guitar and 16 play both How many of the musicians play only piano
Answers
Answer:
4 only play piano
Step-by-step explanation:
12 + 16 = 28
32 - 28 = 4
Find the value of z if the volume of the cylinder is 1696.5m^3 use 3.14 for pi and round your answer to the nearest whole number.
Answers
Answer:
6 m
Step-by-step explanation:
The missing dimension can be found using the volume formula with the known values filled in. This gives an equation that can be solved for z.
The volume of a cylinder is given by the formula ...
V = πr²h
__
Using the given values, we have ...
1696.5 m³ = 3.14(z²)(15 m)
z² = (1696.5 m³)/(47.1 m) ≈ 36.0191 m² . . . . divide by 47.1 m
Taking the square root, we find z to be ...
z ≈ √(36.0191 m²) ≈ 6.00 m
The value of z is about 6 m.
Part 1 - Application
If the length of an arc of a circle of radius 7 is approximately 10.99 cm. What is the measure of the central
angle associated with the arc? Use 3.14 for It. Give your answer in degrees and radians (approximate to two
decimals and exact).
Answers
The measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have a length of an arc of a circle of radius 7 is approximately 10.99 cm.
The radius r = 7 cm
The arc length l = 10.99 cm
We know,
l = rθ
θ is the central angle.
θ = l/r = 10.99/7 = 1.57 radians
To convert 1.57 radians into the degree multiply it by 180/π
θ = 89.95 degree
Thus, the measure of the central angle is 89.95 degree or 1.57 radians if the radius of the circle is 7 cm.
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I need help on this 1 question. Thank you.
Answers
Answer: 5/6, 3/4, 4/12
Step-by-step explanation:
Convert them all into a common denominator, 12.
5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4
1.How many more pupils go to school by tricycle than bicycle?
A.4
B.5
C.3
D.2
2.what is the total number of pupils in grade 6 Simplicity?
A.33
B.28
C.29
D.30
3.what fraction of the pupil in grade 6 Simplicity walk to school?
A.8/33
B.12/33
C.10/33
D.3/33
4.what percentage of the pupil goes to school by walking?
A.24%
B.33%
C.9%
D.36%
Answers
A. 33
B. 12/33
D. 36%
I need help, please. I don’t understand
Answers
Answer:
60%
Step-by-step explanation:
So, this question is saying the bowls can be between a diameter of 6.95 and 7.05
Box 1, 3 and 5 are in this margin.
Box 2 and 4 are not.
3/5 boxes can be included.
3/5 is 6/10
6/10 is 60%
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answers
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
Select the correct answer.
One leg of a right triangle is 10 units, and its hypotenuse is 12 units. What is the length of the other leg?
A.
about 7 units
B.
about 15 units
C.
about 25 units
D.
about 122 units
E.
about 224 units
Answers
solve w^2 + 7w - 18 = 0
with the steps pls
Answers
Answer:
w=2 w = -9
Step-by-step explanation:
w^2 + 7w - 18 = 0
We can factor this equation
What 2 numbers multiply to -18 and add to 7
9*-2 = -18
9+-2 = 7
(w-2) (w+9) = 0
Using the zero product property
w-2 = 0 w+9 =0
w=2 w = -9
Answer:
[tex]w_1=2\\w_2=-9[/tex]
Step-by-step explanation:
This is going to be solved using the quadratic formula.
1. Determine the quadratic equation’s coefficient [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].
Use the standard form, [tex]ax^2+bx+c=0[/tex] , to find the coefficients of our equation,
[tex]w^2+7w-18=0[/tex]:
a = 1
b = 7
c = -18
2. Plug these coefficients into the quadratic formula
The quadratic formula gives us the roots for [tex]aw^2+bw+c=0[/tex] , in which [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are numbers (or coefficients), as follows:
[tex]w=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
7 additional steps:
a = 1
b = 7
c = -18
[tex]w=\frac{-7\pm\sqrt{7^2=4*1*-18} }{2*1}[/tex]
Simplify exponents and square roots
[tex]w=\frac{-7\pm\sqrt{49-4*1*-18} }{2*1}[/tex]
Perform any multiplication or division, from left to right:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2*1}\\w=\frac{-7\pm\sqrt{49--72}}{2*1}\\\\w=\frac{-7\pm\sqrt{49+72}}{2*1}\\w=\frac{-7\pm\sqrt{121}}{2*1}[/tex]
to get the result:
[tex]w=\frac{-7\pm\sqrt{49-4*-18}}{2}[/tex]
3. Simplify square root [tex]\sqrt{121}[/tex]
Simplify 121 by finding its prime factors:
121 ( 11 * 11)
The prime factorization of 121 is 11^2
Write the prime factors:
[tex]\sqrt{121}=\sqrt{11\cdot 11}[/tex]
Group the prime factors into pairs and rewrite them in exponent form:
'[tex]\sqrt{11\cdot 11}=\sqrt{11^2}[/tex]
Use the rule [tex]\sqrt{x^2=x}[/tex] to simplify further:
[tex]\sqrt{11^2}=11[/tex]
4. Solve the equation for w
[tex]w=\frac{-7\pm11}{2}[/tex]
The ± means two answers are possible.
Separate the equations:
[tex]w_1=\frac{(-7+11)}{2}[/tex] and [tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_1=\frac{-7+11}{2}[/tex]
[tex]w_1=\frac{4}{2}[/tex]
[tex]w_1=2[/tex]
[tex]w_2=\frac{-7-11}{2}[/tex]
[tex]w_2=\frac{-18}{2}[/tex]
[tex]w_2=-9[/tex]
---------------------
Why learn this
In their most basic function, quadratic equations define shapes like circles, ellipses and parabolas. These shapes can in turn be used to predict the curve of an object in motion, such as a ball kicked by football player or shot out of a cannon. When it comes to an object’s movement through space, what better place to start than space itself—with the revolution of planets around the sun in our solar system. The quadratic equation was used to establish that planets’ orbits are elliptical, not circular. Determining the path and speed an object travels through space is possible even after it has come to a stop: the quadratic equation can calculate how fast a vehicle was moving when it crashed. With information like this, the automotive industry can design brakes to prevent collisions in the future. Many industries use the quadratic equation to predict and thus improve their products’ lifespan and safety.---------------
Terms and topics
Solving quadratic equations using the quadratic formulaSimplifying radicalsFind prime factors-----------
Learn more:
https://brainly.com/question/1214333https://brainly.com/question/13603021What is the exact value of x
Answers
Answer:
The value of x is 30 degrees.
Step-by-step explanation:
We know that angle 1 is 60 degrees, and that angle two is a right angle (meaning 90 degrees.) 60+90 is equal to 150 degrees. 180 degrees - 150 degrees is equal to 30 degrees. I hope this helps! :)
[tex]~~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\\implies \sin 60^{\circ} = \dfrac{x}{8}\\\\\\\implies x = 8 \sin 60^{\circ}\\\\\\\implies x = 8 \cdot \dfrac {\sqrt3}2\\\\\\\implies x = 4\sqrt 3[/tex]
Which lists all of the x-intercepts of the graphed
function?
O (0, 6)
O (1, 0) and (2, 0)
O (1, 0), (2, 0), and (-3, 0)
O (1, 0), (2, 0), (-3, 0), and (0, 6)
Answers
Answer:
(1, 0), (2, 0), and (-3, 0)
Step-by-step explanation:
The x intercepts are where it crosses the x axis. It crosses at (-3,0), (1,0) and (2,0)
helppp quickkkkkkk enough points
Answers
Answer:
[tex]a=2\\\\ b = 20\\\\ c = 47[/tex]
Step by step explanation:
[tex]a(x) = 2(x+5)^2 -3\\\\~~~~~~~=2(x^2 +2 \cdot 5 \cdot x +5^2) -3\\\\~~~~~~~=2(x^2 +10x+25) -3\\\\~~~~~~~=2x^2 +20x +50 -3 \\\\~~~~~~~=2x^2 +20x +47\\\\\text{By comparing}~ 2x^2 +20x +47~ \text{with the standard form}~ ax^2 +bx+c,\\\\a=2,~ b = 20,~ c = 47[/tex]
Answer:
A or 57 7/9ft3
Step-by-step explanation:
13/3x10/3x4/1 = 520/9=57 7/9
Suppose you have the following null and alternative hypothesis
Answers
A type I error takes place if a given null hypothesis is rejected but is said to be true in the population such as the forecast shows it is snowing outside but actually it is isn't.
What is type 11 error?A type II error is known to be a statistical term that tells the error that takes place when one fails not to accept a null hypothesis that is said to be really false. A type II error create a false negative.
It known is known also as an error of omission. Example is the forecast shows that It is not snowing but it is actually snowing.Note that:
Type I error is false positive.Type II error is false negative.The power of the test shows that:
The Power is the likelihood of rejecting the null hypothesis even if it is false.Power is the likelihood of making the right decision that is to reject the null hypothesis even if the null hypothesis is false.Power is the likelihood of not making a Type II error and others.See full question below
Suppose you have the following null and alternative hypothesis:
H o: it is snowing.
H a: It is not snowing
(A) in the context of this problem, describe a Type-1 error
(B) Describe Type II error
(C)Describe power of the test
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You have been given data about gas prices in 15 states. Comparing the two data sets below, what does the larger standard deviation, range, and variance say about gas prices in 2022 compared to gas prices in 2018?
Gas Prices in 2018 Gas Prices in 2022
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.11
Max: $5.87
Min: $4.48
Mean: $4.83
Median: $4.72
Mode: $4.72
Variance: 0.0142
Standard Deviation: $0.38
Answers
Comparing the two data sets shown below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
Both the mean and the median can be used to describe where the “center” of a dataset is located.
So, the mean of data in 2022 is more than mean of data in 2018.
It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.
As the variance of 2022 more than in variance in 2018.
A high variance indicates that the data points are very spread out from the mean, and from one another.
As the standard deviation of 2022 more than in standard deviation in 2018.
The high standard deviation indicates data are more spread out.
The bigger the range, the more spread out the data.
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DO,K = (9, 6) (3, 2) The scale factor is
Answers
Using proportions, it is found that the scale factor of the transformation is of 1/3.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, during the transformation, each coordinate was divided by 3, hence, applying the proportion, the scale factor of the transformation is of 1/3.
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Anyone mind helping me solve this inequality? Step by step
Answers
By decomposing the figure in simpler shapes, we will see that the total area is:
a = 180 cm²
How to find the area of the composite figure?
Remember that the area of a rectangle of width W and length L is:
A = L*W
And the area of a triangle with base B and height H is:
A = B*H/2.
Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.
So the area of that part is:
A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²
Now, the bottom triangle has a base of 12 cm, and a height of:
15cm - 6cm = 9cm
Then its area is:
A' = 12cm*9cm/2 = 54cm²
This means that the total area of the figure is:
total area = 54cm² + 54cm² = 108cm²
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Samuel can type 40 words per minute. How many hours would it take him to type
2.6 x 10^5 words?
Answers
Answer:
108 1/3 hours
Step-by-step explanation:
There are 60 minutes in 1 hours.
40 words/minute × 60 = 2400 words/hour
2.6 × 10^5 / 2400 = 108.3333... = 108 1/3
Answer 108 1/3 hours
Find the exact length of side a.
Answers
The exact length of a which is equivalent to BC is 7units
Cosine ruleA triangle is a shape with 3 sides and angles. In order to determine the sides BC, we will use the cosine rule
c² = a² + b² - 2abcosC
Given the following parameters
b = 2
c = 5√3
theta = 30 degrees
Substitute
c² = 2² + (5√3)² - 2abcos30
c² = 4 + 75 - 2(2)(5√3)*√3/2
c² = 79 - 30
c² = 49
c = 7 units
Hence the exact length of a which is equivalent to BC is 7units
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The amount of parts, p, that a shop produced in d days is shown in the table below.
d
1 2 3 4 5
p(d) 66 132 240 326 455
Select the average rate of change for the number of parts that the company produced from day 1 to day 3.
87
91
66
146
Answers
Using it's concept, it is found that the average rate of change for the number of parts that the company produced from day 1 to day 3 is of 87.
What is the average rate of change?It is given by the change in the output divided by the change in input.
In this problem, in 2 days, from day 1 to day 3, the number of parts increased from 66 to 240, hence the rate of change is given by:
r = (240 - 66)/2 = 87.
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A pre-school has 12 four-year old children and 11 three-year old children. What is the ratio of four-year old
children to three-year old children?
Answers
Answer:
12:11
Step-by-step explanation
Answer:
I think it would be 12:11
Step-by-step explanation:
This is because you can't down size the 11
Help pls!
Which rational function has zeros at x = -1 and x = 6 ?
Answers
Answer:
[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
Step-by-step explanation:
Let's factorize the 1st option :
⇒ [tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
⇒ [tex]f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}[/tex]
⇒ [tex]f(x) = \frac{(x+1)(x-6)}{(x+2)(x-2)}[/tex]
===============================================================
Finding the zeros :
⇒ Factors of numerator should be equated to 0
x + 1 = 0 ⇒ x = -1x - 6 = 0 ⇒ x = 6=============================================================
Solution :
[tex]f(x) = \frac{x^{2} -5x-6}{x^{2} -4}[/tex]
Answer:
first option
Step-by-step explanation:
the zeros are determined by the numerator of the rational function.
given that the zeros are x = - 1 and x = 6 , then the corresponding factors are
(x + 1) and (x - 6) , that is
(x + 1)(x - 6) ← expand using FOIL
= x² - 5x - 6
the rational function is then
f(x) = [tex]\frac{x^2-5x-6}{x^2-4}[/tex]
If a male student is selected at random, what is the probability the student is a freshman?
Answers
The probability that the student selected at random is a freshman is; 29%
How to find the Probability?
From the given table;
Total number of male students = 4 + 6 + 2 + 2 = 14
Number of freshmen students = 4 students
Thus;
Probability that the student selected at random is a freshman is;
P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%
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The histogram shows the results of a survey that asked people how many hours of sleep they get each night. Which
statements are true?
Answers
The true statements are
The mean is near the median.
The mean is the best measure of center.
The five-number summary is the best measure of variation
What is a histogram?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
If the mean is greater than the median, the histogram would be skewed to the right. If the mean is less than the median, the histogram would be skewed to the left.
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liz wants to determine which sport students like to play the most at her school.which method will most likely produce a random example.
Answers
Answer:
Random sampling
Step-by-step explanation:
Random sampling is a method of choosing a sample of observations from a population to make assumptions about the population. It is also called probability sampling.
Choose the graph below that matches the equation: =2/3 + 5
Answers
It is TRUE, so shade on the SAME side as (0,0)
Given the two rectangles below. Find the area of the shaded region. 4 4 9 3
Answers
Answer:
60
Step-by-step explanation:
The shaded region's area is the difference between the area of the outer rectangle and the white rectangle.
area = LW - lw
area = (4 + 4)(9 + 3) - (4)(9)
area = (8)(12) - 36
area = 96 - 36
area = 60